Apparatus and method for the non-destructive measurement of hydrogen diffusivity

ABSTRACT

Apparatuses and methods of measuring a hydrogen diffusivity of a metal structure including during operation of the metal structure, are provided. A hydrogen charging surface is provided at a first location on an external surface of the structure. In addition, a hydrogen oxidation surface is provided at a second location adjacent to the first location on the external surface of the structure. Hydrogen flux is generated and directed into the metal surface at the charging surface. At least a portion of the hydrogen flux generated by the charging surface is diverted back toward the surface. A transient of the diverted hydrogen fluxes measured, and this measurement is used to determine the hydrogen diffusivity of the metal structure in service.

FIELD OF THE INVENTION

The present invention relates to material inspection and in particularrelates to apparatuses and methods for non-destructive measurement ofhydrogen diffusivity.

BACKGROUND OF THE INVENTION

Hydrogen embrittlement is a phenomenon in which mechanical properties ofmetallic materials, such as tensile strength and ductility, deterioratedue to the uptake of hydrogen. Such degradations decrease the fractureresistance of metals such as steel.

The hydrogen atom ranks as the smallest in diameter among the elements.Hydrogen atoms are easily adsorbed on metal surfaces from which theydiffuse into the interior by jumping between the interstitial latticesof tetrahedral/octahedral sites. Hydrogen can be also trapped atmetallurgical defects and imperfections in steel such as grainboundaries, dislocations, inclusions etc. Once atomic hydrogen isabsorbed, it may precipitate at high-stress zones such as defects,inclusions, voids or discontinuities where a recombination reaction cantake a place. The recombination can cause embrittlement, leadingeventually to cracking. As hydrogen accumulates, linkage of suchhigh-stress zones allows cracks to propagate through the metal.

Hydrogen diffusivity (D_(H)) is a property of the metal determines therate at which hydrogen travels in the material and plays a major role inhydrogen damage development. Hydrogen damage such as hydrogen-inducedcracking is likely to grow faster in high diffusivity materials due toan increased pressure build-up rate. Therefore, accurate knowledge ofD_(H) for a specific material of interest is a crucial input to hydrogendamage evolution models and lifetime prediction tools.

The review of the related art shows that there is a significantdiscrepancy between published values of D_(H) even for the same steelgrade (see table 1). For example, for X65 pipeline steel, reportedvalues of diffusivities range from 10⁻⁵ cm²/s to 10⁻⁷ cm²/s, which is avariation of two orders of magnitude. The large discrepancies can beexplained by multiple factors such as the difference in steelmicrostructure, specimen thickness, surface preparation and permeationtest conditions.

TABLE 1 STEEL EXPERIMENTAL HYDROGEN DIFFUSIVITY TYPE METHOD at 25 C.(cm2/s) X65 Permeation 9.49 × 10⁻⁷  X52 X70 Permeation 0.1-0.9 ×10⁻⁷     0.1-0.3 × 10⁻⁷     X100 Permeation 1.04 × 10⁻⁸  X80 Permeation5.32 × 10⁻⁹  X70 Permeation 2.63 × 10⁻⁷  X65 Permeation 1.5 × 10⁻⁶ X120Permeation 2.0-2.8 × 10⁻⁷     X65 Permeation 0.8-2.7 × 10⁻⁹     X-52Permeation 7 × 10⁻⁷ to 3.2 × 10⁻⁵ X-60 Permeation 5.6-11.5 × 10⁻⁷   X-65 0.9-4.6 × 10⁻⁷     X-80 4.7 × 10⁻⁷ X-100 3.9 × 10⁻⁷ X-65 4.2 × 10⁻⁷X-85 4.0 × 10⁻⁷ X-60 Permeation 3.5 × 10⁻⁶

Due to this large variability in measured D_(H) values, it is importantthat D_(H) be measured directly on a portion of the metallic structureof interest to ensure accuracy. The directly measured value of D_(H) canthen be used as an input to a prediction model. The main challenge forsuch direct measurement is that the standard measurement technique, asdescribed in ISO 17081, is destructive in nature, as it requiresextracting and machining a test specimen from the equipment of interest.Obtaining a test specimen in this manner is usually impossible forinstalled and operational metallic structures.

The standard technique of ISO 17081 is based on the use of theelectrochemical cell of Devanathan and Stachurski, shown in FIG. 1A. Anelectrochemical cell 100 includes a charging cell 110 and an oxidationcell 120. The charging cell 110 includes a platinum auxiliary (counter)electrode 114 and a calomel reference electrode 118. Similarly, theoxidation cell 120 includes a platinum auxiliary (counter) electrode 124and a calomel reference electrode 128. A sample 130 is placed betweenthe charging cell 110 and the oxidation cell 120. In operation, thecharging cell 110 induces generation of hydrogen on the side of thesample surface 130 exposed to the charging cell. Some of the hydrogengenerated on the charging cell side diffuses through the sample to theoxidation cell 120, where the hydrogen atoms are oxidized. The oxidationprocess is facilitated by keeping the sample 130 at a positive potentialof around (+300 mV) against the standard calomel electrode 118. The useof palladium coating at the exit side can enhance the oxidation processfurther. The oxidized hydrogen is measured at an outlet port as afunction of the oxidized current density. From the curve of oxidationcurrent over time, D_(H) is typically calculated using the time lagmethod.

The time lag method is appropriate for determining D_(H) over a singledimension, e.g., the diffusivity of hydrogen from one side of a specimento the other. It is derived from the one-dimensional diffusion equation.The analytical solution for the transient permeation flux is provided inISO-17081 as:

$\begin{matrix}{\frac{J_{perm}(t)}{J_{SS}} = {1 + {\sum\limits_{n = 1}^{\infty}\; {( {- 1} )^{n}{\exp ( {{- n^{2}}\pi^{2}\tau} )}}}}} & (1)\end{matrix}$

where J_(perm)(t) is the transient permeation flux, J_(SS) is the steadystate permeation flux (i.e, J_(SS)=J_(perm)(t=∞)) and τ is thenormalized time expressed as function of the diffusion coefficient andthe specimen thickness L as follows:

$\begin{matrix}{\tau = \frac{D_{H}}{{tL}^{2}}} & (2)\end{matrix}$

A plot of the normalized permeation flux

$( \frac{J_{perm}}{J_{SS}} )$

versus normalized time τ is illustrated in FIG. 1B (with a log scale onthe time axis). The usefulness of this curve (hereafter referred to asthe ‘standard master curve’) is that it is independent of the hydrogencharging concentration C₀, the specimen thickness L, and the hydrogendiffusivity D_(H). In other words, for any hydrogen permeationexperiment that satisfies the one-dimensional conditions shown in FIG.1A, a plot of

$( \frac{J_{perm}}{J_{SS}} )$

vs. τ will stick to this standard master curve. Tabulated values of thiscurve are provided in the ISO standard 17081, such that if the specimenthickness L and the permeation transient J_(perm)(t) are known, thehydrogen diffusivity D_(H) can be easily determined from any point onthe curve. In practice, the point on the curve where

$\frac{J_{perm}}{J_{\infty}} = 0.63$

is commonly used. This point corresponds to a normalized time

$\tau = {\tau_{lag} = {\frac{1}{6}.}}$

The physical time corresponding to τ_(lag) is noted t_(lag) and istherefore by definition equal to

$t_{lag} = {\frac{6L^{2}}{DH}.}$

From the latter the hydrogen diffusivity D_(H) is easily derived as:

$\begin{matrix}{{DH} = \frac{L^{2}}{6t_{lag}}} & (3)\end{matrix}$

The standard technique discussed above requires a test specimen andaccess to both sides of the specimen. As noted, this technique is notapplicable to determining hydrogen diffusivity of metal structures inthe field or to multi-dimensional hydrogen permeation flux. There istherefore a need for a non-destructive measurement technique able tocarry out on-site and in-service measurement of hydrogen diffusivity asrequired. The embodiments of the present invention address this need.

SUMMARY OF THE INVENTION

According to one aspect of the present invention, a method of measuringa hydrogen diffusivity of a metal structure is provided. A hydrogencharging surface is provided at a first location on an external surfaceof the structure. In addition, a hydrogen oxidation surface is providedat a second location adjacent to the first location on the externalsurface of the structure. Hydrogen flux is generated and directed intothe metal surface at the charging surface. A portion of the hydrogenflux is diverted from the metal surface toward the oxidation surface atwhich a current representative of a transient of the hydrogen flux isdetected. The transient of the hydrogen flux used to determine thehydrogen diffusivity of the metal structure. The hydrogen chargingsurface is produced by a first electrochemical cell and the hydrogenoxidation surface is produced by a second electrochemical cell. In someimplementations, the method further comprises measuring an oxidationcurrent in the oxidation cell in order to measure the transient.

In some embodiments, a coating is added at the oxidation surface topromote oxidation of hydrogen. The coating can include depositedpalladium or a palladium foil.

In some embodiments of the method of measuring hydrogen diffusivity,hydrogen diffusivity is determined from the transient of hydrogen fluxusing a direct simulation technique based on a Fickian diffusion modelthat uses initial conditions based on an experimental apparatus.Implementations of these embodiments include setting a value for thehydrogen diffusivity, executing the diffusion model using the set valueof hydrogen diffusivity, comparing results of the Fickian diffusionmodel to results using the experimental apparatus, and repeating theprevious steps with different values of hydrogen diffusivity until aclosest match between the results of the diffusion model and the resultsusing the experimental apparatus is reached.

In alternative embodiments of the method for measuring hydrogendiffusivity, hydrogen diffusivity is determined using a simulated mastergraph for a particular experimental apparatus design, the simulatedmaster graph independent of geometric dimensions, and experimentalparameters. Implementations of these embodiments include performingsensitivity analysis on each parameter to determine an influence of theparameter on a normalized transient permeation curve, and identifyingthe curve as a master curve, with respect to a parameter, if the curveis invariant to changes in the parameter. The parameters can includehydrogen charging concentration, hydrogen diffusivity of the metalstructure, and general geometric parameters of the apparatus design suchas metal structure thickness, a size of the charging surface, a width ofthe oxidation surface and a wall thickness of the charging cell.

According to another aspect of the present invention, an apparatus formeasuring a hydrogen diffusivity of a metal structure is provided. Theapparatus comprises a first chamber positioned on an external surface ofthe metal structure, the first chamber including a hydrogen chargingcell that generates hydrogen at a hydrogen charging surface fordiffusing into the external surface of the metal structure, and a secondchamber separated by a wall from and adjacent to the first chamber andpositioned on the external surface of the metal structure, the secondchamber including an oxidation cell that generates an oxidation surfacefor receiving hydrogen flux diverted from the metals structure. Ameasurement of hydrogen diffusivity is derivable from a hydrogenoxidation current within the oxidation cell.

In some embodiments, the apparatus further comprises a palladium coatingpositioned at the oxidation surface for promoting oxidation of thepermeated hydrogen.

According to embodiments of the apparatus of the present invention, thehydrogen charging cell includes a first electrolyte solution and theoxidation cell includes a second electrolyte solution, both the firstand second electrolyte solutions being in contact with the externalsurface of the metal structure. In some implementations, a first counterelectrode is positioned in the hydrogen charging cell, and a secondcounter electrode and a second reference electrode are positioned in theoxidation cell. A first electric power supply is coupled to the hydrogencharging cell and operative to provide a constant current, and a secondelectric power supply is coupled to the oxidation cell and operative toprovide a constant voltage. The reference electrode located in theoxidation cell maintains a constant potential, and is used to gauge thequality of measurements taken.

Some embodiments of the apparatus may be implemented using an innercasing enclosing the hydrogen charging cell, and an outer casingenclosing the inner casing and the oxidation cell, the oxidation cellpositioned between the inner casing and the outer casing. In furtherimplementations, an alignment element positioned is between the innercasing and the outer casing to ensure that the inner chamber isconcentric within the outer chamber.

In alternative embodiments, the apparatus may be implemented using aninner casing enclosing the oxidation cell, and an outer casing enclosingthe inner casing and the hydrogen charging cell, the hydrogen chargingcell positioned between the inner casing and the outer casing. Infurther implementations, an alignment element positioned is between theinner casing and the outer casing to ensure that the inner chamber isconcentric within the outer chamber.

Further embodiments of the apparatus according to the present inventionincludes a first sealing element for preventing leakage of the firstelectrolyte solution, a second sealing element for preventing leakage ofthe second electrolyte solution. In some implementations, the sealingelement comprises a magnet.

These and other aspects, features, and advantages can be appreciatedfrom the following description of certain embodiments of the inventionand the accompanying drawing figures and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a front cross-sectional view of an apparatus for determiningthe hydrogen diffusivity of a metal material according to the prior art.

FIG. 1B is a graph of normalized permeation flux

$( \frac{J_{perm}}{J_{SS}} )$

versus normalized time τ according to the prior art.

FIG. 2A is a schematic cross-sectional illustration of a wall of a metalstructure permeated by a hydrogen flux according to the presentinvention via a charging surface and oxidation surface.

FIG. 2B shows an exemplary graph of a charging current over time appliedat the charging surface of FIG. 2A.

FIG. 2C shows an exemplary graph of oxidation current over time measuredfor three different metallic materials.

FIG. 3A is a top cross-sectional view of an apparatus for measuringhydrogen diffusivity according to an exemplary embodiment of the presentinvention that employs a hydrogen flux sensor.

FIG. 3B a side cross-sectional view of the apparatus of FIG. 3A

FIG. 3C is top cross-sectional view of another embodiment of anapparatus for measuring hydrogen diffusivity according to the presentinvention that employs a hydrogen flux sensor.

FIG. 3D is a side cross-sectional view of the apparatus of FIG. 3C.

FIG. 3E is a cross-sectional view of the apparatus of FIG. 3Bimplemented with a commercial hydrogen flux sensor.

FIG. 3F is a cross-sectional view of the apparatus of FIG. 3Bimplemented with an ion pump for measuring hydrogen flux.

FIG. 3G is a side cross-sectional view of another embodiment of anapparatus for measuring hydrogen diffusivity according to the presentinvention that employs a hydrogen flux sensor.

FIG. 3H is a top cross-sectional view of another embodiment of anapparatus for measuring hydrogen diffusivity according to the presentinvention that employs a hydrogen flux sensor.

FIG. 3I is a graph showing experimental results of detected hydrogenflux over time using the apparatus of FIGS. 3A, 3B.

FIG. 4A is a top cross-sectional view of an apparatus for measuringhydrogen diffusivity according to an exemplary embodiment of the presentinvention that employs electrochemical cells for charging and oxidation.

FIG. 4B a side cross-sectional view of the apparatus of FIG. 4A

FIG. 4C is a top cross-sectional view of another embodiment of anapparatus for measuring hydrogen diffusivity according to the presentinvention that employs electrochemical cells for charging and oxidation.

FIG. 4D is a side cross-sectional view of the apparatus of FIG. 4C.

FIG. 4E is a top cross-sectional view of another embodiment of anapparatus for measuring hydrogen diffusivity according to the presentinvention that employs electrochemical cells for charging and oxidation.

FIG. 4F is a side cross-sectional view of the apparatus of FIG. 4E.

FIG. 4G is a side cross-sectional view of another embodiment of anapparatus for measuring hydrogen diffusivity according to the presentinvention that employs electrochemical cells for charging and oxidation.

FIG. 5 is a schematic illustration of exemplary boundary conditions fora method of determining hydrogen diffusivity using the direct simulationtechnique according to an embodiment of the present invention.

FIG. 6 shows an exemplary result of the direct simulation techniqueaccording to the present invention. A distribution of hydrogenconcentration C and the streamlines of hydrogen flux throughout thespecimen thickness are illustrated.

FIG. 7A is a graph of hydrogen flux (permeation) over time for severaldifferent values of C₀; FIG. 7B is a graph of the normalized hydrogenflux over time for the same values of C₀.

FIG. 8 is a flow chart of a method for determining hydrogen diffusivityusing the standard master graphs simulation technique according to anembodiment of the present invention.

FIG. 9 shows results of a simulation of hydrogen flux for the apparatusof FIGS. 3A, 3B by varying the value C₀ and keeping other parametersconstant according to the simulated master graphs technique of thepresent invention.

FIG. 10 shows results of a simulation of hydrogen flux for the apparatusof FIGS. 3A, 3B by varying the value D_(H) and keeping other parametersconstant according to the simulated master graphs technique of thepresent invention.

FIG. 11 shows results of a simulation of hydrogen flux for the apparatusof FIGS. 3A, 3B by varying the value R_(ch) and keeping other parametersconstant according to the simulated master graphs technique of thepresent invention.

FIG. 12 shows results of a simulation of hydrogen flux for the apparatusof FIGS. 3A, 3B by varying the value W_(ox) and keeping other parametersconstant according to the simulated master graphs technique of thepresent invention.

FIG. 13 shows results of a simulation of hydrogen flux for the apparatusof FIGS. 3A, 3B by varying the value L_(cc) and keeping other parametersconstant and keeping other parameters constant according to thesimulated master graphs technique of the present invention.

FIG. 14 shows results of a simulation of hydrogen flux for the apparatusof FIGS. 3A, 3B by varying the value L and keeping other parametersconstant and keeping other parameters constant according to thesimulated master graphs technique of the present invention.

FIG. 15 shows a graph including a set of master curves for the apparatusof FIGS. 3A, 3B be generated for different values of L_(cc)/L accordingto the simulated master graphs technique of the present invention.

DETAILED DESCRIPTION

By way of overview, embodiments of the present invention use part of theexternal surface of a metal structure to be investigated as a hydrogencharging surface, and an adjacent part of the external surface as anoxidation surface. Hydrogen atoms are generated at the charging surface,enter the metal, and then a portion of the generated hydrogen atomsdiffuse toward the oxidation surface in a three-dimensional streampattern. By measuring the transient flux over time of the total hydrogencollected at or near the oxidation surface, the hydrogen diffusioncoefficient D_(H) can be determined using embodiments of a simulationmethod adapted for two or three-dimensional hydrogen flux.

When hydrogen penetrates the metal at the charging surface, it tends todiffuse to low chemical potential (i.e., low hydrogen concentration)areas at a speed that is proportional to the gradient of hydrogenconcentration. In other words, hydrogen tends to leave the metal bytaking the “shortest chemical path”. In metallic structures used inindustry having wall thicknesses higher than a millimeter, the shortestchemical path is not necessarily through the thickness of wall from theouter surface to the inner surface. Instead, complex three-dimensionaldiffusion patterns occur. FIG. 2A is a schematic cross-sectionalillustration of a wall of a metal structure 205, permeated by a hydrogenflux according to the present invention via a charging surface 210 andoxidation surface 215. Hydrogen flux lines, e.g., 220 are shown whichillustrate semi-circular paths hydrogen atoms follow as they emanatefrom the charging surface 210 into the metal 205 and then diffuselaterally and upwardly toward the oxidation surface 215. Embodiments ofthe present invention utilize these flux patterns to extract and measurethe residual hydrogen leaving the metal structure 205 from the externalwall near the charging surface 210. Since this residual hydrogendiffuses in the metallic structure at a hydrogen diffusivity D_(H) thatis characteristic (i.e., a property) of the metallic material (withproper surface preparation, surface effects are negligible), the timethat elapses from the start of the hydrogen flux up to the time that theflux reaches a steady state level at the oxidation surface 215, referredto as the “transient,” is correlated with and can be used to determinethe D_(H) of the metal.

FIG. 2B shows an exemplary graph of a charging current over time appliedat charging surface 210; FIG. 2C shows an exemplary graph of oxidationcurrent over time measured for three different metallic materials. Thecurrent shown in FIG. 2B jumps from zero immediately to a steady currentlevel, while the oxidation currents shown in FIG. 2C ramp up relativelyquickly or slowly, depending on the diffusivities of the differentmetallic materials (D_(H1), D_(H2), D_(H3)), up to a steady state level.It is noted that while the steady state levels of oxidation current arethe same for all three curves, the curves 232, 234, 236 for the periodsin which the oxidation current ramps up from zero up to the steady statelevel (i.e., the transient curve), are different for each metal. A highdiffusivity is associated with a short transient time and a sharp curve,while a low diffusivity is associated with a longer transient time and aslowly rising curve. FIG. 2C therefore illustrates that in order todetermine the different hydrogen diffusivities (D_(H1), D_(H2), D_(H3))of the different materials, it is the respective transient curves fromwhich hydrogen diffusivities are derived.

The present invention provides two different groups of apparatuses forobtaining measurements of hydrogen flux transients. In the first groupof embodiments, a hydrogen flux probe is placed in proximity to thecharging surface for exposure to diverted streams of hydrogen flux. Insome embodiments, the hydrogen flux probe measures the flux of hydrogenwith a selective detector for H2, e.g. FID. In the second group ofembodiments, two electrochemical cells are employed to generate anoxidation current, and the transient of an oxidation current is used aproxy for the hydrogen flux variation. In both sets of embodiments, thehydrogen flux is measured or derived over time to determine thetransients of the hydrogen flux prior to reaching steady state level.

Hydrogen Flux Probe Embodiments

FIG. 3A is a top cross-sectional view and FIG. 3B is a sidecross-sectional of a first embodiment of an apparatus fornon-destructive measurement of D_(H) according to the principlesdisclosed herein. Referring to FIG. 3B, which shows the apparatus 300installed on a surface of a metal to be tested, the apparatus 300includes an outer casing 305 made of an electrically insulating materialthat is also chemically resistant to mildly acidic electrolytes (e.g.,electrolytes of pH in the range of 3.5 to 4.5). Exemplary materials thatmeet these qualifications include polymeric compounds such aspolypropylene (PP), polyethylene (PE), polymethyl-methacrylate (PMMA),polyvinylidene fluoride (PVDF), polytetrafluoro-ethylene (PFTE),polyimide 11 (PA 11) and polyetheretherketone (PEEK). The outer casing305 is hollow and can be cylindrical in form, although otherconfigurations are possible. An inner casing 310 of a smaller size thanthe outer casing 305 is positioned within the first casing. The innercasing 310 is also electrically insulating and can be made of the sameor similar materials as the outer casing 305. In some implementations,the inner casing 310 is also hollow and can be cylindrical in form. Wheninstalled on the surface of a metal to be tested, it is preferable forthe inner casing 310 to be positioned concentrically within the outercasing 305. Outer chamber 315 is defined as the region between the outercasing 305 and the inner casing 310; inner chamber 317 is defined asregion in the interior of second casing 310. In some implementations, afirst O-ring 307 is set within a groove on the bottom of the outercasing 305. Similarly, in some implementations a second O-ring 312 isset within a groove on the bottom of the inner casing 310.

During a measurement operation, the outer casing 305 and inner casing310 are placed and onto the external surface 320 of a metal structureand sealed with respect to the surface by O-rings 307, 312. Once theinterface between the bottom of casings 305, 310 and the surface 320 issealed, the outer chamber 315 is filled substantially (e.g., 70-90percent of the chamber volume) with an electrolyte solution 325 shown asdashed lines within the outer chamber. The electrolyte 325 thus comesinto direct contact with the surface 320 of the metal structure ofinterest at the bottom of outer chamber 315. The interface between theelectrolyte 325 and the metal surface 320 is termed the “chargingsurface”. In this arrangement, the metal surface itself acts as aworking electrode. A range of electrolyte solutions can be employeddepending on the target level of hydrogen changing and duration of thehydrogen permeation measurement performed. A buffer can be used tomaintain constant pH throughout a measurement. Exemplary solutionsinclude 0.1/1M sodium hydroxide, 3.5% sodium chloride, and 0.1Msulphuric acid solutions.

A counter electrode 330 is positioned within the electrolyte 325 in theouter chamber 315. In some embodiments, the counter electrode 330comprises a platinum mesh. In other embodiments, to reduce costs, carbonelectrodes or other suitable electrodes that do not react with theelectrolyte solution 325 at the applied potential can be used. In someembodiments, a reference electrode 335, used to measure voltage, is alsopositioned in outer chamber 315. Any suitable commercially availablereference electrode can be used, including a Calomel electrode orsilver-silver chloride electrode. However, use of a reference electrodein the charging cell is optional and not required. An annular lid 340conforms to and fits over the outer chamber 315 and couples to the outercasing 305 and inner casing 310. In some implementations, the lid 340 iscoupled to the outer and inner casings 305, 310 through one or moreO-rings to ensure containment of electrolyte 325. Referring to FIG. 3A,the lid 340 includes holes 342 through which leads can be extended to orfrom the counter electrode 330 and reference electrode 335.

An electric power supply 345 is coupled at a negative terminal to themetal surface 320, at a positive terminal to a lead of counter electrode330. In some embodiments, the power supply 345 also includes a neutralterminal to a lead of reference electrode 335, Throughout the presentdisclosure, it should be understood that the charging apparatus can alsobe a simple DC with metal at the negative pole and a counter electrodeat the positive pole, with no need for a reference electrode, which isoptional. The electric power supply 345 preferably runs in galvanostat(i.e., constant current) mode in order to maintain a constant currentbetween the metal surface 320 (working electrode) and the counterelectrode 330. The constant current induces electrolysis and generationof hydrogen atoms at the interface between metal surface 320 andelectrolyte 325. A fraction of hydrogen atoms evolve as dihydrogen andof this fraction, a certain sub-fraction penetrates into the metal. Ifthe metal surface is of sufficient thickness, e.g., greater than onemillimeter, the hydrogen entering the metal surface diffuses in complexflux patterns based on concentration gradients. Some of the hydrogenflux is diverted toward inner chamber 317.

Positioned within the inner chamber 317 is a hydrogen flux sensor 350,such as a hydrogen flux sensor, operative to detected hydrogen fluxdiverted into the inner chamber 317. In some embodiments, a commerciallyavailable hydrogen flux probe is employed. An example of a suitablehydrogen flux probe is the Hydrosteel 6000 instrument manufactured byIonScience of Cambridge, UK. The hydrogen flux sensor is selected tohave a sufficient sensitivity to detect approximately 1 pl/cm²/s. A viewof an implementation of the apparatus according to FIGS. 3A, 3Bspecifically including a Hydrosteel 6000 instrument 391 and accompanyinggas conduit 392 is shown in FIG. 3E.

FIGS. 3C and 3D depict a top cross-sectional view and a sidecross-sectional view of another embodiment of an apparatus for measuringhydrogen diffusivity having a different geometrical configuration.Apparatus 360 includes a single casing 365 that is divided into firstand second chambers 370, 372 by a wall 375. The casing 360 isrectangular in form, as are the first and second chambers 370, 372. Inthis embodiment, a counter electrode 377 and an optional referenceelectrode 378 (which can be similar to the first embodiment of FIGS. 3A,3B) are positioned in the second chamber 372. The second chamber 372 isfilled with an electrolyte solution 380. The electrolyte solution 380directly contacts the surface of metal structure 320. Hydrogen fluxsensor 382, including gas outlet port 384 is positioned at the bottom ofthe first chamber 370 so as to receive hydrogen flux streams divertedtoward the first chamber 370. A galvanostat 385 (or alternatively, asimple DC power supply) is coupled to the metal surface 320, counterelectrode 377 and reference 378 as in the embodiment of FIGS. 3A and 3B.The galvanostat 385 generates a charging current that induces generationof hydrogen atoms in the electrolyte which then diffuse into the metalsurface 320. A lid 387 conforms to and covers the first and secondchambers 370, 372, and includes a first opening 388 for the gas outletport 384 and further openings 389, 390 for passing leads of the counterelectrode 377 and reference electrode 378.

In general, the apparatuses of FIG. 3A-3D are adaptable so as to be usedwith a variety of commercially available hydrogen flux sensors, and thegeometrical designs of the chambers can be configured to suit thecharacteristics of desired hydrogen flux sensors in specificapplications. For example, FIG. 3F is a view of an implementation of theapparatus according to FIGS. 3A, 3B that includes an inlet for an ionpump 393 instead of a hydrogen flux sensor. The ion pump (not shown inFIG. 3F) creates a vacuum and the current required to maintain thevacuum gives an indication of the hydrogen flux.

Additional embodiments of an apparatus for measuring hydrogendiffusivity are shown in FIGS. 3G, 3H and 3I. The apparatus shown inFIG. 3G is identical to the apparatus 300 of FIG. 3B except for theaddition of a sealing element 396 that is included to ensure thecomplete sealing of the charging and oxidation cells on the metalsurface. The sealing element 396 can be implemented as a magnet (asshown), or for small structures, as a strap to mechanically secure thecell to the apparatus to the structure to be tested. FIG. 3H is across-sectional view of another embodiment which is also identical tothe apparatus 300 of FIGS. 3A, 3B with the addition of an alignmentelement used to ensure alignment between the outer casing and innercasing. In the depicted implementation, the alignment element cancomprise a hollow annular insert having ribs, e.g., 399 that can preventrelative movement between the inner and outer casings. In anotherimplementation, the alignment element can comprise a groove in the lid(not shown).

In operation, if the metal structure to be tested includes anon-metallic coating, the coating is removed to allow direct contactbetween at least the charging surface of the apparatus and the metalsurface. However, if the interface between metallic surface and coatingand the coating itself are hydrogen permeable, the coating does not needto be removed from the oxidation surface portion area on the structuresurface. After any such preliminary preparation, the apparatus is firstinstalled on the surface of the metal structure. The electrolyte is thenadded to the outer chamber. The negative electrode of the electric powersupply is connected to the metal structure (working electrode) and thepositive electrode to the counter electrode. The reference electrode isconnected to the Galvanostat. A constant current is then applied betweenthe counter electrode. The hydrogen flux sensor is used to measure thehydrogen flux as it changes over time (the transient) within the innerchamber. A suitable method is then employed to derive the hydrogendiffusivity of the metal from the measured hydrogen flux transient.

Experiments performed with the apparatus 300 of FIGS. 3A, 3B show thatthe apparatus is able to detect high hydrogen flux even at low currentdensity. A graph of hydrogen flux over time taken during one suchexperiment is shown in FIG. 3J. The high yield of detected hydrogen fluxmakes modeling simpler, and enables use of less sensitive hydrogen fluxsensors in the apparatus. As shown in the figure, testing can beperformed over an extended period to reach a final steady state current(e.g., about 25-30 hours).

The embodiments of the apparatus that include a hydrogen flux sensor(probe) described above have a number of benefits and advantages. Theapparatus can be used to determine the hydrogen diffusion coefficient(D_(H)) of metals equipment in the field, without damage to theequipment. Application of the apparatus requires little surfacepreparation, and does not require use of expensive palladium foils orcoatings. Moreover, embodiments of the apparatus can be combined withother hydrogen flux measurement techniques and existing commercialdevices. As noted above, use of platinum for counter electrodes in thecharging cell is not compulsory. Alternative electrodes, such as carbonelectrodes, can be used so long as they do not react with theelectrolyte solution of the charging cell.

Electrochemical Probe Embodiments

FIG. 4A is a top cross-sectional view and FIG. 4B is a sidecross-sectional of another embodiment of an apparatus fornon-destructive measurement of D_(H) according to the principlesdisclosed herein. Referring to FIG. 4B, which shows the apparatus 400installed on a surface of a metal to be tested, the apparatus 400includes two electrochemical cells, a charging cell 410 and an oxidationcell 420. Charging cell 410 cell is positioned in an inner chamber 411enclosed within an inner casing 412. The inner casing is, in turn,positioned within an outer casing 414. An outer chamber 415 ispositioned between the inner casing 412 and the outer casing 414. Boththe outer casing 414 and inner casing 412 are made of an electricallyinsulating material that is also chemically resistant to mildly acidicelectrolytes (e.g., electrolytes of pH in the range of 3.5 to 4.5).Exemplary materials that meet these qualifications include polymericcompounds such as polypropylene (PP), polyethylene (PE),polymethyl-methacrylate (PMMA), polyvinylidene fluoride (PVDF),polytetrafluoro-ethylene (PFTE), polyimide 11 (PA 11) andpolyetheretherketone (PEEK). In the embodiment of FIG. 4B, the inner andouter casings 412, 414 are hollow and can be cylindrical in form,although other configurations can be used. When installed on the surfaceof a metal to be tested, it is preferable for the inner casing 412 to bepositioned concentrically within the outer casing 414. Inner chamber 411contains an electrolyte solution 416 that is in direct contact with theexternal surface 430 of a metallic structure to be tested. The interfacebetween the electrolyte 416 and the metal surface 430 is termed the“charging surface”. A range of electrolyte solutions can be employeddepending on the target level of hydrogen changing and duration of thehydrogen permeation measurement performed. A buffer can be used tomaintain constant pH throughout a measurement. Exemplary solutionsincluding a 0.1/1M sodium hydroxide, 3.5% sodium chloride, and 0.1Msulphuric acid solutions.

A counter electrode 417, which functions as the cathode of the chargingcell, and an optional reference electrode 418, used for accurate voltagemeasurement, are positioned in the electrolyte 416. In someimplementations, counter electrode 417 is a platinum mesh similar tothose used in standard electrochemical cells. The reference electrode418 can be implemented as a standard calomel electrode. In order tocontain the electrolyte 416 within inner chamber 411, an O-ring 419 iscoupled to the bottom of the inner casing 412, and an O-ring 419 iscoupled to the bottom of the outer casing 414 by insertion in a groove(not shown). An electric DC power supply 440 operable to provide aconstant current is coupled at a negative terminal to metal surface 430,at a positive terminal to counter electrode 417, and, in embodiments inwhich a reference electrode is employed, at a neutral terminal toreference electrode 418. The power supply 440 generates a potentialdifference between the metal surface 430 and the counter electrode 417which induces an ionic current, and also causes a certain amount ofhydrolysis of water molecules at the metallic surface. A fraction ofhydrogen atoms evolve as dihydrogen and a sub-fraction of this fractionpenetrates/diffuses into the metal.

An oxidation cell 420 is positioned in the outer chamber 415 ofapparatus 400. Oxidation cell 420 includes a counter electrode 421 and areference electrode 422 positioned within outer chamber 415. Counterelectrode 421 and reference electrode 422 can be implemented usingsimilar materials as those used for counter electrode 417 and referenceelectrode 418, respectively. The outer chamber 415 is filled with anelectrolyte solution 423 which directly contacts metal surface 430 at an“oxidation surface”. Electrolyte solution 423 can but does not have tohave the same characteristics as the electrolyte 416 of the chargingcell 410. In some implementations, a 0.1/1M sodium hydroxide solutioncan be used for the electrolyte 423, although a wide range of othersolutions can be used. In order to contain the electrolyte 423 withinouter chamber 415, an O-ring 424 is coupled to the bottom of the outercasing 414. An electric power supply 445 operable to provide a constantvoltage (voltage source mode) is coupled at a positive terminal to metalsurface 430, at a negative terminal to counter electrode 421, and at aneutral terminal to reference electrode 422 by insertion in a groove(not shown).

A coating 450, which is preferably made of palladium, is deposited onthe oxidation surface of the metal that is in contact with theelectrolyte 423 of oxidation cell 420. The coating 450 promotesoxidation of hydrogen atoms that reach the oxidation surface. Thecoating can be prepared in any of the ways know to those of skill in theart. A lid 460 conforms to and fits over both the inner chamber 411 andouter chamber 415. Referring to FIG. 4A, the lid 460 includes a firstpair of openings 461, 462 positioned when the lid is in place over theinner chamber 411 to allow electrical leads to couple counter electrode417, and reference electrode 418, to electric power supply 440.Similarly, lid 460 includes a second pair of openings 463, 464 to allowelectrical leads to couple the counter electrode 421 and referenceelectrode 422 to electric power supply 445.

FIGS. 4C and 4D depict a top cross-sectional view and a sidecross-sectional view of another embodiment of an apparatus for measuringhydrogen diffusivity in which the positions of charging cell and theoxidation cell are switched. Referring to FIG. 4D, the apparatus 470includes two electrochemical cells, an oxidation cell 475 and a chargingcell 485. Oxidation cell 475 is positioned in an inner chamber 471enclosed within an inner casing 472. The inner casing 472 is, in turn,positioned within an outer casing 474. Charging cell 485 is positionedin outer chamber 476 positioned between the inner casing 472 and outercasings 474. Both the inner casing 472 and the outer casing 474 are madeof an electrically insulating material that is also chemically resistantto mildly acidic electrolytes such as those described above with regardto the apparatus of FIGS. 4A and 4B.

Inner chamber 475, which comprises the oxidation cell, contains anelectrolyte solution 477 that is in direct contact with the externalsurface 490 of a metallic structure to be tested. In someimplementations, a 0.1/1M sodium hydroxide solution can be used for theelectrolyte 477, although a wide range of other solutions can be used.The bottom of inner casing 472 can include or be coupled to a sealingelement such as an O-ring 481 to prevent leaking of the electrolyte 477.The interface between the electrolyte 477 and the metal surface 490 isin this embodiment the oxidation surface. A coating 484, which ispreferably made of palladium, is deposited on the oxidation surface ofthe metal that is in contact with the electrolyte 477 of oxidation cell475. A counter electrode 478 and a reference electrode 479 arepositioned in the electrolyte solution 477. An electric power supply 495operable as a constant voltage source is coupled at a positive terminalto the metal surface 490, at a negative terminal is coupled to counterelectrode 478 and at a neutral terminal is coupled to referenceelectrode 479. Outer chamber 485, which comprises the charging cell,also includes an electrolyte solution 486 which may be similar to thesolution used for the charging cell described above with reference toFIGS. 4A, 4B. The bottom of outer casing 474 can include or be coupledto a sealing element such as an O-ring 482 to prevent leaking of theelectrolyte 486. The interface between the electrolyte 486 and the metalsurface 490 is in this embodiment is the charging surface. A counterelectrode 487 and a reference electrode 488 (optional) are positioned inelectrolyte solution 486. An electric power supply 497 operable as aconstant current source is coupled at a positive terminal to the metalsurface 490, at a negative terminal to counter electrode 487, and,optionally, at a neutral terminal to reference electrode 488. A lid 483conforms to and fits over both the inner chamber 471 and outer chamber476 and includes openings (not shown) for electrical leads to theelectrodes of the apparatus 470.

It is noted that the electric power supplies 440, 445, 495, 497 in theembodiments depicted are coupled to and controlled by a computing device(not shown) which can modify the respective applied current and voltagesto achieve accurate hydrogen detection.

A further embodiment of an apparatus for measuring hydrogen diffusivityaccording to the present invention is shown in FIGS. 4E and 4F. Theapparatus 491 is similar in configuration to the apparatus shown inFIGS. 3C and 3D above (i.e., rectangular and double-chambered), thedifference being that the apparatus 491 includes both a charging cell492 and an oxidation cell 493. Otherwise, the apparatus of FIGS. 4E and4F are similar to the other electrochemical cell embodiments describedwith reference to FIGS. 4A-4D. Another embodiment of an apparatus formeasuring hydrogen diffusivity 498, shown in FIG. 4G is identical to theapparatus 300 of FIG. 4B except for the addition of a sealing element499 that is included to ensure the complete sealing of the charging andoxidation cells on the metal surface. The sealing element 499 can beimplemented as a magnet, or for small structures, as a strap tomechanically secure the cell to the apparatus to the structure to betested.

In operation, if the metal structure to be tested includes anon-metallic coating, the coating is removed. After such preliminarypreparation, the apparatus is first installed on the surface of themetal structure. Electrolyte is then added to the oxidation cell. Thevoltage between the oxidation surface of the working electrode and thereference electrode of the oxidation cell is then set using the electricpower supply configured in constant voltage mode at approximately +300mV. Once the oxidation current I_(ox) in the oxidation cell hasstabilized, electrolyte is added to the charging cell. A constantcharging current is then set using the electric power supply configuredin Galvanostat mode. Once the charging current has started, thetransient of the oxidation current (I_(ox)) at the oxidation cell, whichis representative of the hydrogen flux, is monitored until a steadystate is reached. A suitable method is then employed to derive thehydrogen diffusivity of the metal from transient of the oxidationcurrent.

Methods of Determining Hydrogen Diffusivity

Since the standard time lag method developed under a one-dimensionaldiffusion approximation cannot be used for determine D_(H) for themulti-dimensional hydrogen streams, the present invention provides botha 1) direct simulation method and 2) a simulated master graph method todetermine D_(H).

Direct Simulation Method

In the direct simulation method, an optimization problem in which thehydrogen diffusion kinetics approximated by a Fickian diffusion modelwith apparent diffusivity D_(H) is solved at each optimization step (forexample using finite element) with a different value of D_(H)(incremental approach). In other words, the direct simulation methodsimulates and best fits the field results for every single fieldmeasurement (or also called the inverse problem). The direct simulationmethod can employ finite element analysis technique in this method. Thisiterative simulation is stopped, and the optimum D_(H) is reached, whenthe best fit between the numerically simulated permeation curve and theexperimentally measured one is obtained.

The diffusion model to be solved at each iteration is given in Eq. 4. Aset of boundary conditions and initial conditions, which depend on theapparatus design and service conditions, are associated to Eq. 4.

$\frac{\partial C}{\partial t} = {{D_{H}\Delta^{2}C} = {D_{H}( {\frac{\partial^{2}C}{\partial x^{2}} + \frac{\partial^{2}C}{\partial y^{2}} + \frac{\partial^{2}C}{\partial\; Z^{2}}} )}}$

The boundary conditions associated with, for example, the apparatus 300of FIGS. 3A, 3B design are shown in FIG. 5. The boundary conditionsinclude the hydrogen charging concentration (C₀), the thickness of themetal tested (L), the wall thickness of the charging cell (L_(cc)), theradius of the charging surface (R_(ch)) (more generally, the size of thecharging surface), and the width of the oxidation surface (W_(ox)). Atypical solution of the above boundary value problem is illustrated inFIG. 6, which illustrates a distribution of hydrogen concentration C andthe streamlines of hydrogen flux throughout the specimen thickness.

In this optimization, the boundary value for the hydrogen chargingconcentration (C₀) provided by the charging cell is arbitrary, and doesnot influence the value of the normalized steady-state permeation fluxat the oxidation surface. This is illustrated by comparison of FIG. 7Awith FIG. 7B. FIG. 7A is a graph of hydrogen flux (permeation) over timefor several different values of C₀. As shown, the steady statepermeation is different for the various values of C₀. FIG. 7B is a graphof the normalized hydrogen flux over time for the same values of C₀. Ascan be discerned, FIG. 7B shows a single curve, indicating that thenormalized flux converges to the same values for all of the values ofC₀. In other words, the optimization problem shall be carried outconsidering the normalized flux rather than the actual flux.

Simulated Master Graphs Method

In the simulated master graphs method, a series of “master curves” aregenerated for a particular apparatus design. The master curves can thenbe used to determine the value of D_(H) from the measured permeationtransients. Once developed for a given apparatus design, the mastergraphs become characteristic of the specific design. In this section, aset of master curves are derived from the apparatus design of FIGS. 4A,4B. However, the same methodology can be applied for other apparatusdesigns as well, and none of the following description should be takenas limiting the method to a specific design.

By definition, a master curve is independent of the geometricaldimensions of the apparatus concerned, as well as the thickness of thetested metal surface, the value of the metal's hydrogen diffusivity, andthe hydrogen charging concentration. To obtain master curves that areindependent of these parameters, the following procedure is carried out.First, all of the parameters that have an influence on the measuredpermeation transient J_(perm)(t) are listed. A sensitivity analysis isthen carried out on each parameter by varying one parameter at a time todetermine the influence of each parameter on a plot of

$( \frac{J_{perm}}{J_{SS}} )\; {{vs}.( {\tau = \frac{DH}{{tL}^{2}}} ).}$

If the plot (termed the “normalized permeation transient (NPT) plot”)remains invariant while the parameter is varied, then the plot isconsidered to be a master curve. If the plot does not remain invariant,then the parameter of the x-axis is changed, and, if needed,restrictions on the variability of the test parameters are introduced.This procedure is described in greater detail below.

FIG. 8 is a flow chart of an embodiment of a method 800 for determininghydrogen diffusivity using standard master graphs according to thepresent invention. This flow chart is tailored to the apparatusdescribed in FIGS. 4A and 4B, and in general the specific parameterstested can vary depending on the apparatus design employed including itsphysical parameters. In a first step 810, parameters that can influencethe permeation transient are listed. The parameters can include, forthis embodiment, the radius of the hydrogen charging surface (R_(ch)),the width of the oxidation surface (W_(ox)), the thickness of the metaltested (“specimen”) (L) and the wall thickness of the charging cell(L_(cc)). In a following step 820, each parameter is fixed to areference value. A table of exemplary reference values is given in Table2 below.

TABLE 2 Parameter Reference Value Variation Range Unit L 10   [5-30] MmR_(ch) L [0.5L-5L] Mm W_(ox) L [0.5L-5L] Mm L_(cc) L/2 [0.5L-2L] Mm

In step 840, the value of R_(ch) (radius of the charging surface) isvaried over different values within a variation range, while keeping allother parameters constant. At each variation increment, in step 842, aparametric simulation is performed based on the R_(ch) value. Results ofexperimental simulations by varying R_(ch) are shown in FIG. 11. Withrespect to this variable, when the value of R_(ch) is increased to orabove the specimen thickness (i.e., R_(ch)≥L), the NPT plot becomesinvariant to further increases in R_(ch). Accordingly, the NPT can beconsidered a master curve provided that R_(ch)≥L.

In step 844, the value of W_(ox) (width of the oxidation surface) isvaried over different values within a variation range, while keeping allother parameters constant. At each variation increment, in step 846, aparametric simulation is performed based on the Wox value. Results ofexperimental simulations by varying W_(ox) are shown in FIG. 12. Likethe Rch parameter, when Wox is increased to or above the specimenthickness (W_(ox)≥L), the NPT plot becomes invariant to furtherincreases in W_(ox). Accordingly, the NPT can be considered a mastercurve provided that W_(ox)≥L.

In step 848, the value of L_(cc) (wall thickness of the charging cell)is varied over different values within a variation range, while keepingall other parameters constant. At each variation increment, in step 850,a parametric simulation is performed based on the L_(cc) value. Resultsof experimental simulations by varying L_(cc) are shown in FIG. 13. Asindicated in FIG. 13, the NPT plot shows a clear dependence on the valueof L_(cc) (i.e., it is not invariant with respect to L_(cc)). Thisdependence can be explained by the fact that the width of the chargingcell has a substantial effect on the shortest path that hydrogen cantravel to reach the oxidation surface.

Similarly, in step 852, the value of L (thickness of the metal specimen)is varied over different values within a variation range, while keepingall other parameters constant. At each variation increment, in step 854,a parametric simulation is performed based on the L value. Results ofexperimental simulations by varying L_(cc) are shown in FIG. 14. FIG. 14indicates that the NPT is also not invariant with respect to L, whichalso affects the shortest path for hydrogen diffusion.

By employing a ratio of L_(cc) to L (i.e., L_(cc)/L), the two variableswhich affect the NPT plots can be converted into a single controllingparameter for the position of the master curve. Provided that theconditions, R_(ch), W_(ox)≥L, a set of master curves can be generatedfor different values of L_(cc)/L. For the apparatus 400 of FIGS. 4A, 4B,a set of hydrogen permeation master curves are shown in FIG. 15.Tabulated values of the curves are presented in Table 3.

TABLE 3 L_(cc)/L τ 1/6 1/5 1/4 1/3 1/2 1 2 0.01 0.05 0.03 0.01 0 0 0 00.02 0.13 0.09 0.05 0.02 0 0 0 0.03 0.20 0.16 0.11 0.06 0.01 0 0 0.040.27 0.22 0.16 0.10 0.03 0 0 0.05 0.32 0.28 0.22 0.14 0.05 0 0 0.06 0.370.33 0.27 0.18 0.08 0 0 0.07 0.42 0.37 0.31 0.23 0.11 0.01 0 0.08 0.460.42 0.36 0.27 0.14 0.01 0 0.09 0.50 0.46 0.40 0.31 0.18 0.02 0 0.100.54 0.49 0.43 0.35 0.21 0.03 0 0.15 0.68 0.65 0.60 0.53 0.39 0.12 00.20 0.78 0.76 0.72 0.67 0.55 0.26 0.02 0.25 0.86 0.84 0.81 0.77 0.690.42 0.07 0.30 0.91 0.90 0.88 0.85 0.79 0.56 0.15 0.40 0.97 0.96 0.950.94 0.91 0.79 0.38 0.50 0.99 0.99 0.99 0.98 0.97 0.91 0.63 0.60 1 1 10.99 0.99 0.97 0.81 0.70 1 1 1 1 1 0.99 0.90 0.80 1 1 1 1 1 0.99 0.960.90 1 1 1 1 1 1 0.99 1.0 1 1 1 1 1 1 1

It is noted that in some embodiments, it is possible to substitute adifferent parameter for the abscissa parameter

$( {\tau = \frac{D_{H}}{{tL}^{2}}} )$

in order to generate a single master curve for all values of Lcc.However, it is preferable in many instances to keep the abscissaparameter for the sake of overall consistency with the standard plot ofISO-17081.

Returning to FIG. 8, in step 855 the master curves are assembled foreach of the parameters (for those parameters that are invariant, the NPTplot is used as the master curve). In step 860, once the master curvesare generated, they can be used to determine the value of D_(H) using anexperimentally measured hydrogen flux transient. While any point on themaster curve can be used, it is common to use the point on the curvewhere

$\frac{J_{perm}}{J_{\infty}} = {0.63.}$

D_(H) can then be calculated from

$D_{H} = \frac{\tau_{lag}L^{2}}{t_{lag}}$

where the value t_(lag) is determined from the experimental measurement.The value of τ_(lag) is determined directly from the master curvecorresponding to the experimental value of L_(cc)/L. Tabulated values ofτ_(lag) for different master curves (i.e., different values of L_(cc)/L)are shown in Table 4. The method then ends in step 870.

TABLE 4 L_(cc)/L 1/6 1/5 1/4 1/3 1/2 1 2 τ_(lag) 0.13 0.14 0.16 0.190.22 0.33 0.5

The disclosed apparatus and methods provide several advantageousfeatures. Prominently, the disclosed apparatus and methods provide fordetermination of hydrogen diffusivity of metal equipment while theequipment is in operation, namely when the metallic structure issubjected to internal pressure (hoop stress etc.) and processtemperature.

Some of the methods disclosed herein are intended to be implementedusing a programmed computer system. The flowchart and block diagramsillustrating such methods can represent a module, segment, or portion ofcode, which comprises one or more executable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative implementations, the functions noted in theblock may occur out of the order noted in the figures. For example, twoblocks shown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

It is to be understood that any structural and functional detailsdisclosed herein are not to be interpreted as limiting the systems andmethods, but rather are provided as a representative embodiment and/orarrangement for teaching one skilled in the art one or more ways toimplement the methods.

It should be understood that although much of the foregoing descriptionhas been directed to systems and methods for implanting photonicmaterials, methods disclosed herein can be similarly deployed other‘smart’ structures in scenarios, situations, and settings beyond thereferenced scenarios. It should be further understood that any suchimplementation and/or deployment is within the scope of the system andmethods described herein.

It is to be further understood that like numerals in the drawingsrepresent like elements through the several figures, and that not allcomponents and/or steps described and illustrated with reference to thefigures are required for all embodiments or arrangements

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising”, when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

Terms of orientation are used herein merely for purposes of conventionand referencing, and are not to be construed as limiting. However, it isrecognized these terms could be used with reference to a viewer.Accordingly, no limitations are implied or to be inferred.

Also, the phraseology and terminology used herein is for the purpose ofdescription and should not be regarded as limiting. The use of“including,” “comprising,” or “having,” “containing,” “involving,” andvariations thereof herein, is meant to encompass the items listedthereafter and equivalents thereof as well as additional items.

While the invention has been described with reference to exemplaryembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted forelements thereof without departing from the scope of the invention. Inaddition, many modifications will be appreciated by those skilled in theart to adapt a particular instrument, situation or material to theteachings of the invention without departing from the essential scopethereof. Therefore, it is intended that the invention not be limited tothe particular embodiment disclosed as the best mode contemplated forcarrying out this invention, but that the invention will include allembodiments falling within the scope of the appended claims.

1. A method of measuring a hydrogen diffusivity of a metal structurecomprising: providing a hydrogen charging surface at a first location onan external surface of the structure; providing a hydrogen oxidationsurface at a second location adjacent to the first location on theexternal surface of the structure; generating a hydrogen flux directedinto the metal surface at the charging surface; detecting a currentrepresentative of a transient of the hydrogen flux diverted back towardthe oxidation surface form the metal structure; and determining thehydrogen diffusivity of the metal structure based on the detectedhydrogen flux.
 2. The method of claim 1, wherein the hydrogen chargingsurface is produced by a first electrochemical cell and the hydrogenoxidation surface is produced by a second electrochemical cell.
 3. Themethod of claim 2, further comprising adding a coating at the oxidationsurface to promote oxidation of hydrogen.
 4. The method of claim 3,wherein the coating includes palladium.
 5. The method of claim 2,further comprising measuring an oxidation current in the oxidation cellin order to measure the transient.
 6. The method of claim 1, wherein thehydrogen diffusivity is determined from the transient of hydrogen fluxusing a direct simulation technique based on a Fickian diffusion modelthat uses initial conditions based on an experimental apparatus.
 7. Themethod of claim 6, further comprising: setting a value for the hydrogendiffusivity; executing the diffusion model using the set value ofhydrogen diffusivity; comparing results of the Fickian diffusion modelto results using the experimental apparatus; and repeating the previoussteps with different values of hydrogen diffusivity until a closestmatch between the results of the diffusion model and the results usingthe experimental apparatus is reached.
 8. The method of claim 1, whereinthe hydrogen diffusivity is determined from the transient of hydrogenflux using a simulated master graph for a particular experimentalapparatus design, the simulated master graph being independent ofgeometric dimensions, and experimental parameters.
 9. The method ofclaim 8, further comprising: performing sensitivity analysis on eachgeometrical parameter to determine an influence of the parameter on anormalized transient curve; and identifying the curve as a master curve,with respect to a parameter, if the curve is invariant to changes in theparameter.
 10. The method of claim 9, wherein the parameters include atleast two of the following: metal structure thickness, a size of thecharging surface, a width of the oxidation surface and a wall thicknessof the charging cell.
 11. The method of claim 1, wherein the measurementof hydrogen diffusivity is performed while the metal structure is inservice and operational 12-21. (canceled)